Asset and Liability Insurance Management (ALIM) for Risk Eradication
Unlike traditional valuation methods, viability theory provides tools for eradicating risk by determining the minimum initial capital required to meet the commitments of the investor, regardless of forecasted market developments. This capital can play the
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Asset and Liability Insurance Management (ALIM) for Risk Eradication
18.1 Introduction Asset and liability management (ALM) deals with approaches that allow a company to manage the composition of its risky assets or underlying in such a way that they are always larger than its liabilities. Choosing a management rule is a choice under contingent uncertainty (choosing an exposition of the portfolio) and tychastic uncertainty (valid for risky returns above a forecasted lower bound). The objective of portfolio insurance is to enable investors to participate opportunistically in market performance while providing protection of any type of liability against all evolutions of risky prices consistent with a prediction model, at each date up to maturity. The liability is understood in the largest sense, from the standard protection at exercise time or allowing for variable annuities, as in life insurance or retirement pension plans. In other words, portfolio insurance’s main objective is 1. Either to evaluate risk 2. Or to eliminate or limit the loss of portfolio value while allowing the portfolio to benefit opportunistically, to some extent, from a rise in the “market.” Here, we propose to eradicate losses. The motivation for such a strategy is based on the simple observation that during, for example, the crashes of October 1987 and October 1989, strategies such as buy and hold (which fixes the risky part of the portfolio once and for all) or the constant proportion portfolio insurance (CPPI) method (which amounts to keeping constant the “cushion multiplier,” which is the ratio of the expectation over the cushion, or surplus, defined as the difference between the value of the portfolio and the liability). CPPI is a widely used fund management technique and a capital guarantee derivative security that provide participation in the performance of the underlying asset [125] but “. . . could result in very significant losses,” violating the “I” in CPPI. See, for instance, the studies of [50, 54], among several authors. Cont and Tankov point out the fact that the CPPI does not eliminate risk: Yet the possibility of going below the floor, known as “gap risk,” is widely recognized by CPPI managers: there is a P. Bernhard et al., The Interval Market Model in Mathematical Finance, Static & Dynamic Game Theory: Foundations & Applications, DOI 10.1007/978-0-8176-8388-7 18, © Springer Science+Business Media New York 2013
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18 Asset and Liability Insurance Management (ALIM) for Risk Eradication
nonzero probability that, during a sudden downside move, the fund manager will not have time to readjust the portfolio, which then crashes through the floor. In this case, the issuer has to refund the difference, at maturity, between the actual portfolio value and the guaranteed amount. It is therefore important for the issuer of the CPPI note to quantify and manage this “gap risk.” In their paper [50], the authors describe the CPPI in the following way: [. . . ] An alternative approach [. . . ] based on the following two ideas: first
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